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6p+5t=-16 and 3p-3=3t












































addition and substitution methods for solving linear equations

Solve the following system of equations for p and t using the addition method or the substitution method.

6p + 5t = -16

3p - 3 = 3t


Verify your answers by substituting the solutions for p and t into the original equations.

Comments for 6p+5t=-16 and 3p-3=3t

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May 09, 2014
solve for the unknown variables p and t
by: Staff


Answer


Part I


1st equation: 6p + 5t = -16

2nd equation: 3p - 3 = 3t


Solve the system of linear equations





Explanation:

Solving for p and t using the addition elimination method

We are going to multiply the 2nd equation by 2 and then subtract it from the 1st equation.

Multiplying by 2 will change the first term in the 2nd equation to 6p, which is also the first term in the 1st equation.

When we subtract the 2nd equation from the 1st equation, the variable p will be eliminated.

This will leave us with an equation with only one variable (the variable t) to solve.


Solution:

Multiply the second equation by 2

3p - 3 = 3t

2 * (3p - 3 = 3t)

2 * (3p – 3) = 2 * 3t


Expand the left side of the equation using the distributive law

2 * (3p – 3) = 2 * 3t

2 * 3p + 2 * (– 3) = 2 * 3t

6p - 6 = 6t


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May 09, 2014
solve for the unknown variables p and t
by: Staff

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Part II


 Addition elimination method:

     1.  multiply both sides of the second equation by 2

     2.  remove the parentheses using the distributive law





Subtract 6t from each side of the equation

6p - 6 = 6t

6p - 6 - 6t = 6t - 6t

6p - 6t - 6 = 6t - 6t

6p - 6t - 6 = 0


Add 6 to each side of the equation

6p - 6t - 6 = 0

6p - 6t - 6 + 6 = 0 + 6

6p - 6t + 0 = 0 + 6

6p - 6t = 6





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May 09, 2014
solve for the unknown variables p and t
by: Staff


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Part III


Simplify the equation:

     1.  subtract 6t from each side of the equation

     2.  add 6 to each side of the equation     

*** Click to enlarge image ***





The result obtained by multiplying the second equation by 2 is :

6p - 6t = 6


Subtract the result from the first equation

1st equation: 6p + 5t = -16

Result obtained by multiplying the second equation by 2:

6p - 6t = 6

6p + 5t = -16

- (6p - 6t = 6)
-------------------
?

6p + 5t = -16

- 6p + 6t = - 6
-------------------
0 + 11t = -22

11t = -22


Eliminate the variable p:  subtract the second equation from the first equation 

*** Click to enlarge image ***






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May 09, 2014
solve for the unknown variables p and t
by: Staff


----------------------------------------------------------------


Part IV


Divide each side of the equation by 11

11t = -22

11t / 11 = -22 / 11

t * (11 / 11) = -22 / 11

t * (1) = -2

t = -2


Solve for t:  divide each side of the equation by 11  

*** Click to enlarge image ***





substitute -2 for the value of t in the first equation, and then solve for p

6p + 5t = -16

6p + 5 * (-2) = -16

6p - 10 = -16


Add 10 to each side of the equation

6p - 10 = -16

6p - 10 + 10 = -16 + 10

6p + 0 = -6

6p = -6


Divide each side of the equation by 6

6p = -6

6p / 6 = -6 / 6

p * (6 / 6) = -6 / 6

p * (1) = -1

p = -1



Solve for p:  substitute -2 for t  

*** Click to enlarge image ***





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May 09, 2014
solve for the unknown variables p and t
by: Staff


----------------------------------------------------------------


Part V


Divide each side of the equation by 6   

*** Click to enlarge image ***




the final answer is:

p = -1

t = -2


Solution to the linear system of equations:

     6p + 5t = -16

     3p - 3 = 3t     

*** Click to enlarge image ***





----------------------------------------------------------------

May 09, 2014
solve for the unknown variables p and t
by: Staff


----------------------------------------------------------------


Part VI


Graphical solution to the linear system of equations:

     6p + 5t = -16

     3p - 3 = 3t     

*** Click to enlarge image ***





----------------------------------------------------

Verify your answers by substituting the solutions for p and t into the original equations.

p = -1

t = -2

1st equation: 6p + 5t = - 16

6 * (-1) + 5 * (-2) = - 16

- 6 - 10 = - 16

- 16 = - 16, OK → p = -1 & t = -2 is a valid solution


2nd equation: 3p - 3 = 3t

3 * (-1) - 3 = 3 * (-2)

- 3 - 3 = - 6

- 6 = - 6, OK → p = -1 & t = -2 is a valid solution







Thanks for writing.

Staff
www.solving-math-problems.com



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